...a given straight line of unlimited length, from a given point without it. 5. If from the ends of a side of a triangle, there be drawn two straight lines...of the triangle, but shall contain a greater angle. 6. The straight lines which join the extremities of two equal and parallel straight lines towards the...

...EUCLID. SECTION I.— 1. If from the ends of the sides of a triangle there be drawn a straight line to a point within the triangle, these shall be less...of the triangle, but shall contain a greater angle. 2. In any right-angled triangle, the square which is described on the side subtending the right angle...

...greater than AB. Therefore any two sides, &c. Q, ED D 4 iii 1. v. 1. xix. 1. BOOK L PROP. XXL THEOR. If from the ends of the side of a triangle there be drawn tiro straight lines to a point within the triangle, these shall be less than the other tico sides of...

...С a greater than a b. Therefore any two sides, ˇfee. QED PROPOSITION XXI. — THEOREM. If from Hie ends of the side of a triangle there be drawn two...contain a greater angle. LET the two straight lines bd, С d be drawn from b, С, the ends of the side b С of the triangle ab С, to the point d within it...

...THIS PAPER.) Section I. 1. If from the ends of the sides of a triangle there be drawn a straight line to a point within the triangle, these shall be less...of the triangle, but shall contain a greater angle. 2. In any right singled triangle, the square which is described on the side subtending the right angle...

...together greater than the third. Which was to be proved. PEOP. XXI. THEOE. If from the extremities of any side of a triangle there be drawn two straight lines to a point within the triangle : then these two straight lines shall together be less than the other two sides of the triangle, and...

...side of a triangle, there be drawn two straight lines to a point within the triangle, these two lines shall be less than the other two sides of the triangle,...two straight lines BD, CD be drawn from B, C, the ends'ot the side BC of the triangle ABC, to the point D within it; BD and DC 'are less than the other...

...same points to any other point in the given straight line. PROP. XXI. THEOREM. If from the ends of one side of a triangle, there be drawn two straight lines to a point within the triangle, these together shall be less than tfte other two sides of the triangle, but shall contain a greater angle....

...of a triangle, there be drawn two straight linen to a point within the triangle, these tti'D lines shall be less than the other two sides of the triangle, but shall contain a greater angle. Produce BD to E; and because two sides of a triangle (20. 1.) are greater than the third side, the...

...to another, and likewise those which are terminated in the other extremity. 2. If from the ends of a side of a triangle there be drawn two straight lines...of the triangle, but shall contain a greater angle. 3. If two triangles have two sides of the one equal to two sides of the other, each to each, and one...